TOPIC: Cell Structure and Function: How to Escape a Jaguar
TUTOR GUIDE
MODULE CONTENT: This module contains simple exercises for biology majors
taking an introductory course in cell and molecular biology. The major goals of
the module are for students to a) use a linear model in a biological context; b)
practice using simple statistical analyses and working with them in Excel; and c)
gain an understanding of the amplification that can occur in cellular signaling
pathways, and its importance. The module includes a review of linear models,
use of similar models and simple mathematics in a cellular signal transduction
model, and simple statistical analysis of data related to the model system.
Throughout, there is the context of amplification within a hormonal signaltransduction system. There is also an opportunity for students to extend this
understanding to a more complicated model in an optional additional exercise
relating to another hormonal system.
The module is designed to be implemented in a 60-minute classroom session
with a preparatory assignment for students to complete and turn in at the
beginning of the session. The module is designed for first-year biology majors in
an introductory biology course. Students at this level often learn the vocabulary
of simple signal transduction systems (“G-protein,” “cAMP” etc.) with few or any
real-life examples, so this module provides an opportunity for students to connect
a specific example to their general knowledge and vocabulary, to see the
importance of amplification in this system, to practice using a simple statistical
test, and to extend the linear modeling skills they have used in other modules, if
such modules are used previous to this one.
TABLE OF CONTENTS
Alignment to HHMI Competencies for Entering Medical Students (Learning
Objectives).............................................................................................................2
Outline of concepts covered, module activities, and implementation……..……....3
Module: Worksheet for completion in class........................................................4-9
Pre-laboratory Exercises (mandatory).................................................................10
Suggested Questions for Formative Assessment.......................................... 11-12
Guidelines for Implementation……………………………...............…...................13
Contact Information for Module Developers........................................................14
1
Alignment to HHMI Competencies for Entering Medical Students:
Competency
E1. Apply quantitative reasoning
and appropriate mathematics to
describe or explain phenomena
in the natural world.
E7: Explain how organisms
sense and control their internal
environment
and how they respond to
external change.
Learning Objective
E1.1 Demonstrate quantitative numeracy
and facility with the language
of
mathematics
Activity
1,2
E1.2. Interpret data sets and communicate
those interpretations using visual and other
appropriate tools.
E1.3. Make statistical inferences from data
sets (evaluating best fit linear relationships
based on calculating error sums of squares)
E1.5. Make inferences about natural
phenomena using mathematical models
E1.7 Quantify and interpret changes in
dynamical systems.
3,4,5,6
E7.2 Explain physical and chemical
mechanisms used for transduction and
information processing in the sensing and
integration of internal and environmental
signals
1,4,5
2
6
5,6
5
Mathematical Concepts covered:
- power functions
- linear models
- t-tests
In class activities:
- group discussion
- graphing in Excel and interpreting data
- construction of linear models
- carrying out t-tests in Excel
Components of module:
- preparatory assignment to complete and turn in as homework before class
- in class worksheet:
- discussion questions
- plotting and interpreting data
- suggested assessment questions
- guidelines for implementation
Estimated time to complete in class worksheet
- 60 minutes
Targeted students:
- first year-biology majors in introductory biology course
Quantitative Skills Required:
- Basic arithmetic
- Logical reasoning
- Interpreting data from tables
- Graph/Data Interpretation
3
WORKSHEET: Cell structure and function
In Class Exercises
Background
When your body needs to respond to an acute stressor, such as a jaguar coming
into the room, the sympathetic nervous system triggers an immediate release of
the hormone epinephrine, also known as adrenaline. Epinephrine travels in the
bloodstream to the liver, where it attaches to specific proteins (receptors) on
liver cell membranes and stimulates those cells to break down glycogen into
glucose and release the glucose into the bloodstream, providing a source of
energy for you to run away from the jaguar.
4
Epinephrine
Receptor
Adenylate cyclase
G-protein
Inactive
cAMP-dept.
protein kinase
Active cAMPdept. protein
kinase
Inactive glycogen
phosphorylase
kinase
Active glycogen
phosphorylase
kinase
Inactive glycogen
phosphorylase
Active gly
phosphor
Glycogen
As you can see, this process involves several steps and most of these steps
involve activation of an enzyme (anything ending in “-ase”!). Recall that enzymes
are not consumed in the reaction they catalzye, so in this case the binding of one
epinephrine molecule to its receptor on the liver cell can result in many glucose
molecules being released.
5
6
Questions
1. Let’s assume that one molecule of epinephrine binding to the cell activates
one G-protein, which activates one adenylate cyclase. From there, assume that
every enzyme catalyzes 10 reactions (for example, each activated adenlylate
cyclase produces 10 molecules of activated cAMP dependent protein kinase).
Finally, assume that each activated glycogen phosphorylase “frees” 10
molecules of glucose to be released from the cell into the bloodstream. Given
that, how many molecules of glucose are released into the blood for each
molecule of epinephrine that binds?
2. Consider that the epinephrine is only present when you see the jaguar, so
prior to that there is no epinephrine to bind. After the epinephrine is in the
bloodstream, the number of bound epinephrine reaches a maximum when all the
receptors are full. Suppose that there are 100 epinephrine receptors on the cell.
Using the ideas of piece-wise linear functions that you developed in the
homework for this module, write an equation for the amount of glucose as a
function of the amount of bound epinephrine.
3. With “number of molecules of epinephrine bound” on the X axis and “number
of molecules of glucose released” on the Y axis, plot the relationship between
these variables, as described by your answer to part 1.
4. Using your graph, explain what biological features of this system dictate the
piecewise linear structure of the graph. Use phrases like “floor” and “ceiling,” and
justify them in the context of the biological system.
5. Now, consider the rate of bloodflow to the muscles both before and after the
jaguar sighting. This is important because the more blood your muscles get, the
more glucose they get, and the faster you can run away! Now suppose that the
veins and arteries are modeled as tubes with constant radius. The bloodflow is
directly proportional to the radius to the fourth power.
a. Write an equation for the bloodflow as a function of radius.
Plot the bloodflow as a function of radius (remember that the radius
is on the x-axis and the bloodflow is on the y-axis)
b. On the same plot, add the graphs of the functions e^x and x^2.
Which graph goes to up faster as x gets large? Which graph goes
to up slowest when x gets large? Do you think that x^5 goes up
faster or slower than x^4?
7
c. If the arteries going to your muscles get twice as wide during a
jaguar sighting (they do!), how much more blood flows through
them (by what factor does blood flow increase)?
6. As part of a study, 10 mg of epinephrine was injected into the bloodstream of
10 resting, fasted adults. 10 minutes later, blood glucose levels of the subjects
were measured. Here were the results:
Subject
Sex
Age
1
2
3
4
5
6
7
8
9
10
F
F
F
F
F
M
M
M
M
M
25
36
61
54
39
43
46
31
51
37
Blood
Glucose
Level, mg/dL
197
175
231
217
205
251
234
181
197
161
Using Excel and the above data, perform a t-test to answer the questions:
a) Did the men have a significantly different glucose level after epinephrine
injection than the women?
b) Did the individuals over 40 have a significantly different glucose level after
epinephrine injection than the individuals under 40?
To do this, enter the relevant data in two columns (e.g. one column for men and
one for women). Then in any blank space, enter the formula:
=TTEST(A2:A10,B2:B10,2,1),
except that instead of A2:A10, type the range of whatever your first group (array)
of data is, and instead of B2:B10, type the range of your second array. The
resulting value will be between 0 and 1. If the value (the p value) is less than
0.05, you can reject the null hypothesis that there is no difference between the
groups you compared, and therefore gained support for the idea that there is a
difference (however, you have not, and cannot, prove that there IS a difference!)
8
MODULE FEEDBACK - Each year we work to improve the modules in the active
learning "discussion" sections. Please answer the following question with regard
to this module on this sheet and turn in your answer to the TA. You can do this
anonymously if you like by turning in this sheet separately from your module
answers.
To what degree did this module HELP YOU UNDERSTAND fundamental
concepts in cell function? Please rate this module on a scale of:
A (excellent - helped a lot) to E (bad - did not help at all).
Module Rating ____________
Thank you!
9
I. Pre-laboratory Exercises
To be handed in (or posted electronically) at the beginning of class.
(For practice using Excel)
1. First we will review equations of lines. Recall the slope-intercept form of the line
is y=mx+b, where m is the slope and b is the y-intercept, and the point-slope version
of the line is (y-y0)=m(x-x0).
a. Write the equation for the line whose value is zero for all values of x.
b. Write the equation of the line whose value is one for all values of x.
c. Write the equation of the line through the points (1, 0) and (2, 1).
d. Now we are going to define a piecewise function using the three previous
equations. This function will take on the value of zero when when 0<x<1, the value
of the line through (1,0) and (2.1) for 1<x<2, and the value of one for x>2. Plot the
line.
2. Plot the following functions in Excel for positive values of x. (If you don't know
how to enter formulas or plot in Excel, open Excel and click on the help icon in
the tool bar at the top to find step by step procedures):
a. y=x
b. y=1/x^2
c. y=e^x (note, in Excel use the command "exp" to substitute for e. For
example, in Excel if you enter the following formula into a cell: = exp(1)
you will get the approximate value of e, 2.718282)
d. y=1/x^4
e. y=1/x^5
Describe the features of each graph. Consider the following questions: What is
the largest value that the function achieves? What is the smallest value that the
function achieves? Are there local maximum or minimums (hills or valleys)?
Which function decreases the fastest to zero for large values of x? Which one
increases the quickest for small (0<x<1) values of x?
10
Assessment Questions:
1. When players take steroid hormones, the steroid hormones travel to muscle
cells and act as transcription factors, activating transcription of genes that make
muscle proteins. If each molecule of hormone triggers the transcription of 1500
mRNAs for the muscle protein myosin, and each mRNA transcript can be used
as the template for translation 8 times before it is degraded, how many new
myosin molecules get built for each molecule of injected steroid?
2. Plot molecules of actin translated (y-axis) against number of steroid molecules
arriving at the muscle cell (x-axis).
3. What is the equation for the steroid-muscle line? Also describe the relationship
between these variables in words.
4. Here is some data for the muscle mass increase of people taking steroids.
Can you reject the null hypothesis that the steroids were not more effective in
increasing the muscle mass of the men than the women?
Subject
Sex
1
2
3
4
5
6
7
8
9
10
F
F
F
F
F
M
M
M
M
M
Increase in
bicep mass, g
0
5
3
11
8
43
46
31
51
37
5. Hormones can act at very low concentrations because:
a) there are many steps in their signaling pathways that involve amplification
b) hormones remain in the bloodstream for very long time periods
c) each individual hormone molecule binds to thousands of different cells
11
d) any change a hormone triggers in its target cell keeps going indefinitely
12
Instructions for Implementation by TAs:
Have the students bring laptops (everyone doesn’t need to bring one). Collect
homework. Have students break up into groups, ideally of 4-5 students each.
From here you can proceed on one of two ways:
1. Give each student group a simple dry-erase board (available for about $3
apiece at office-supply stores), mini-chalkboard, or large piece of paper, and a
marker. Ask each question in the module, one at a time, by projecting the slide
with the question or writing it on the board. Also supply each group with a color
photo of the cell cartoon, so they can refer to it throughout. Some questions also
have introductory content, which is provided on the slides.
Give the students a few minutes with each question or sub-question—not a long
time, no more than 3-4 minutes per question-- and some questions need only a
minute, such as the first two questions. The shorter the interval, the higher the
level of energy and interest in the room. As the students work, circulate and
assist them (without giving them the answer, of course). At the end of the time
period for the question, announce that there are 10 seconds remaining, then ring
a bell or use some other pre-agreed signal, and at the signal, all student groups
hold up their white boards with their answers. Use the boards as a basis for
discussion if answers differ. If most student groups have the right answer, move
on quickly to the next question. The ppt file is provided as part of the module.
2. Alternatively, the questions can all be given together to each student group as
a worksheet. This sounds like less work and stress for the TAs/instructors, but
the one-at-a-time-method keeps everyone on track, energized and having fun.
Try it!
13
Module Developers:
Please contact us if you have comments/suggestions/corrections
Kathleen Hoffman
Department of Mathematics and Statistics
University of Maryland Baltimore County
khoffman@math.umbc.edu
Jeff Leips
Department of Biological Sciences
University of Baltimore County
leips@umbc.edu
Sarah Leupen
Department of Biological Sciences
University of Baltimore County
leupen@umbc.edu
Acknowledgments:
This module was developed as part of the National Experiment in Undergraduate
Science Education (NEXUS) through Grant No. 52007126 to the University of
Maryland, Baltimore County (UMBC) from the Howard Hughes Medical Institute.
14